Lattice Definitions

Every ALPS lattice simulation runs on a graph — a set of sites and the bonds between them — specified in XML. This section builds that XML up in stages: from an arbitrary graph with explicit vertices and edges, through the unit-cell machinery used to describe regular (finite or infinite) lattices, to combining the two into the graph ALPS actually simulates, bundling the result into a reusable library, and finally checking that what you defined is what you meant.

Introduction

Why lattices and graphs need to be specified in an input file at all, an overview of the five HOWTOs below, a reference figure of the most common lattices already built into ALPS, and a pointer to the full ALPS lattice library file (lib/xml/lattices.xml).

Simple Graphs

How to specify an arbitrary graph directly, by listing every <VERTEX> and <EDGE> in XML — no regularity or lattice structure assumed. Covers colored graphs (vertex and edge type attributes, for distinguishing sublattices or bond types) and attaching spatial <COORDINATE>s to vertices.

Lattice and Unit Cells

How to describe a regular lattice compactly, as a unit cell repeated by translation, instead of listing every site by hand. Covers infinite lattices (via <LATTICE> and its basis vectors, which can be numeric or symbolic/parametrized), finite lattices of a given extent (via <FINITELATTICE> and <EXTENT>, with fixed, parametrized, or partially-infinite dimensions), open and periodic <BOUNDARY> conditions, and referencing a previously defined <LATTICE> by name instead of redefining it.

Lattices and Graphs

How to turn a lattice into the actual graph ALPS simulates, by decorating each unit cell with a <UNITCELL> graph (its own vertices and edges, including bonds that cross into neighboring cells) and combining it with a <LATTICE> or <FINITELATTICE> inside a <LATTICEGRAPH> element. Walks through a minimal one-vertex chain and a more complex two-vertex unit cell on a periodic rectangular lattice.

A library of Lattices and Graphs

How to collect named <LATTICE>, <FINITELATTICE>, <UNITCELL>, and <LATTICEGRAPH> definitions inside a single <LATTICES> element, so that a simulation’s input file can refer to a lattice by name (e.g. LATTICE="square lattice") instead of repeating its full definition every time — exactly how the built-in ALPS lattice library is organized.

Check Lattice Graph

How to sanity-check a new lattice definition with the printgraph tool, which generates the graph from a parameter file in exactly the way an ALPS application would generate it internally, so you can confirm it matches what you intended before running a real simulation on it.